Diffusion tensor imaging (DTI) is a magnetic resonance imaging (MRI) technique that measures the directionally dependent rate of water self-diffusion in each image voxel. These measures are in the form of a second-order diffusion tensor (Basser, P. J., Mattiello, J., & LeBihan, D. (1994), MR diffusion tensor spectroscopy and imaging. Biophys J, 66(1), 259-267), which can be decomposed into three non-negative eigenvalues and three eigenvectors that describe the magnitude and orientation of water diffusion in each image voxel. Water diffusion in cerebral white matter tends to be anisotropic due to the highly linear organization of white matter fibers. That is, water will preferentially diffuse more rapidly along white matter tracts because physical barriers such as axonal walls restrict water movement in other directions (see Beaulieu, C. (2002), The basis of anisotropic water diffusion in the nervous system—a technical review, NMR Biomed, 15(7-8), 435-455, and see also Sun, S. W., Song, S. K., Harms, M. P., Lin, S. J., Holtzman, D. M., Merchant, K. M. (2005), Detection of age-dependent brain injury in a mouse model of brain amyloidosis associated with Alzheimer's disease using magnetic resonance diffusion tensor imaging. Exp Neurol, 191(1), 77-85). Medical conditions, such as subcortical ischemic injury, inflammation, neurodegenerative diseases, and traumatic brain injury cause changes in the organization of white matter pathways, often including reductions in its linearity, with corresponding changes in anisotropy as well as the speed and direction of diffusion. DTI is sensitive to these changes making it a powerful in vivo imaging tool for studying the microstructural integrity of cerebral white matter.
The majority of studies using DTI to assess white matter microstructure in clinical samples have been based on two-dimensional greyscale maps of scalar values such as mean diffusivity (MD), a measure of the magnitude of diffusion in each image voxel, and fractional anisotropy (FA), a measure of the extent to which that diffusion is directionally restricted. Generally, these basic scalar measures are derived from the eigenvalues of the multi-valued tensor data and do not incorporate eigenvector information. The scalar values in each image voxel are then mapped to two-dimensional grayscale images. An exception is the use of eigenvector information to produce two-dimensional FA maps in which fiber orientation is mapped to color (for example, see Pajevic, S., & Pierpaoli, C. (1999), Color schemes to represent the orientation of anisotropic tissues from diffusion tensor data: Application to white matter fiber tract mapping in the human brain, Magn Reson Med, 42(3), 526-540, and also Wakana, S., Nagae-Poetscher, L. M., Jiang, H., van Zijl, P., Golay, X., & Mori, S. (2005), Macroscopic orientation component analysis of brain white matter and thalamus based on diffusion tensor imaging, Magn Reson Med, 53(3), 649-657).
Of particular interest to the embodiments of the invention described herein is Westin, C. F., Peled, S., Gubjartsson, H., Kikinis, R., & Jolesz, F. (1997), Geometrical diffusion measures for MRI from tensor basis analysis, Paper presented at the International Society for Magnetic Resonance in Medicine, Vancouver, Canada, where a linear anisotropy measure is shown to be a geometric parameter that is descriptive of diffusion mainly being in the direction of the largest eigenvalue.
Tractography methods complement scalar methods by providing detailed information about the orientation and curvature of white matter pathways within the brain. Tractography methods utilize both the tensor eigenvalues and the eigenvectors to calculate trajectories generally in the direction of the fastest diffusion. The trajectories are then portrayed graphically using curved lines (see Xue, R., van Zijl, P. C., Crain, B. J., Solaiyappan, M., & Mori, S. (1999), In vivo three-dimensional reconstruction of rat brain axonal projections by diffusion tensor imaging, Magn Reson Med, 42(6), 1123-1127) or by using glyphs, such as hyperstreamlines, which were initially proposed by Delmarcelle and Hesselink (1993) as a means of visualizing other types of second-order tensor fields, and then subsequently applied to DT-MRI data by Zhang et al. (Zhang, S., Demiralp, C., & Laidlaw, D. (2003), Visualizing diffusion tensor MR images using streamtubes and streamsurfaces, IEEE Transactions on Visualization and Computer Graphics, 9(4), 454-462). To date, tractography methods have gained the widest acceptance in neuroscience studies that explore white matter connectivity, the effects of pathologies on connectivity, and improvements in data acquisition and visualization methods.
Only a few preliminary methodological studies have explored the utility of combining tractography with quantitative scalar measures (i.e., “quantitative tractography”) for clinical research, where group comparisons are important. For example, Ciccarelli et al. (Ciccarelli, O., Parker, G. J., Toosy, A. T., Wheeler-Kingshott, C. A., Barker, G. J., Boulby, P. A., et al. (2003a), From diffusion tractography to quantitative white matter tract measures: A reproducibility study, Neuroimage, 18(2), 348-359) studied the reproducibility of tract-“normalized” volume (NV) and FA in three white matter pathways traced by a fast marching tractography (FMT) algorithm (see Parker, G. J. (2000), Tracing fibre tracts using fast marching, Proceedings of the International Society of Magnetic Resonance in Medicine, 85; Parker, G. J., Stephan, K. E., Barker, G. J., Rowe, J. B., MacManus, D. G., Wheeler-Kingshott, C. A., et al. (2002a), Initial demonstration of in vivo tracing of axonal projections in the macaque brain and comparison with the human brain using diffusion tensor imaging and fast marching tractography, Neuroimage, 15(4), 797-809; and Parker, G. J., Wheeler-Kingshott, C. A., & Barker, G. J. (2002b), Estimating distributed anatomical connectivity using fast marching methods and diffusion tensor imaging, IEEE Trans Med Imaging, 21(5), 505-512). The results (Ciccarelli et al., 2003a) showed variability in measures of tract volume and fractional anisotropy across different fiber bundles, suggesting that fiber organization has an impact on the reproducibility of tractography algorithms. Ciccarelli et al. (Ciccarelli, O., Toosy, A. T., Parker, G. J., Wheeler-Kingshott, C. A., Barker, G. J., Miller, D. H., et al. (2003b), Diffusion tractography based group mapping of major white-matter pathways in the human brain, Neuroimage, 19(4), 1545-1555) also examined the extent of intersubject variability in the anterior corpus callosum, optic radiations, and pyramidal tracts. They found that the tractography maps corresponded well to known anatomy and that there was greater intersubject variability at the terminal ends of tracts adjacent to cerebral cortex, but lower variability in the core of tracts, and no right-left differences in variability. Ding et al. (2003) (Ding, Z., Gore, J. C., & Anderson, A. W. (2003), Classification and quantification of neuronal fiber pathways using diffusion tensor MRI. Magn Reson Med, 49(4), 716-721) also demonstrated good reproducibility of tractography-based metrics such as curvature, torsion, parallel diffusivity, and perpendicular diffusivity along bundle length. Huang et al. (2005) (Huang, H., Zhang, J., Jiang, H., Wakana, S., Poetscher, L., Miller, M. I., et al. (2005), DTI tractography based parcellation of white matter: Application to the mid-sagittal morphology of corpus callosum, Neuroimage, 26(1), 195-205) have also used quantitative methods for parcellating projections from the corpus callosum to cortical regions. Each of these studies demonstrated the utility of using quantitative tractography.
However, prior to this invention researchers were limited in their ability to pose and address questions concerning the integrity of specific white matter pathways in their entirety (i.e., following the trajectory of the pathway in all three dimensions), and their relationship to cognitive and behavioral changes in a variety of conditions affecting cerebral white matter. Such questions cannot be adequately addressed using conventional region-of-interest approaches with scalar DTI maps. While some earlier quantitative tractography work described above may address some of these limitations, it does not do so adequately.
It is noted that Ciccarelli et al. (Ciccarelli, O., Parker, G. J., Toosy, A. T., Wheeler-Kingshott, C. A., Barker, G. J., Boulby, P. A., et al. (2003a), From diffusion tractography to quantitative white matter tract measures: A reproducibility study, Neuroimage, 18(2), 348-359), discuss normalizing tract volume using the total intercranial volume (see page 352, left column) in a determination of connectivity.